315 
of ‘ Achromatic Object-Glasses . 
For the 3d surface concave flint lens, (See Rule 8. art. 14.) 
Focal length = 4*64, dec. part of index = *601 ; 
4*64 x 601 =r 2*788 . . = 1st product, 
12*06 = given rad. 
2*788 x 12*06 = 33*62328 = dividend, 
12*06 + 2*788 = 14*848 = divisor, 
14*848) 33*62328 (2*26 = rad. 3d surface. 
We have thus the four following radii, for the successive sur- 
faces to a compound focal length of 10 inches, viz. 
Plate -f ^ St Slir ^ ace rac ^ us 6*85 inches convex, 
l 2d surface radius 2*22 inches convex, 
Flint I ^ sur f ace radius 2*26 inches concave, 
l 3d surface radius 12.060 inches convex. 
These, it will be observed, are for a compound focus of 10 
inches, whereas our example required a 46 inch focus. We must 
therefore increase these several radii in the proportion of 10 to 
which gives the following 
As 10 : 46 : : 0*85 
results : 
: 31 '510 1st surface 
convex, 
10 : 46 : 
: 2-22 
: 10-212 2d 
convex, 
10 : 46 : 
: 2-26 
: 10 396 3d 
concave, 
10 : 46 : 
: 12060 
: 55-476 4th 
convex. 
If the circumstance of the second contact surface, that is the 
convex one, being the deeper of the two, should be thought a 
practical inconvenience, or if it should be thought desirable to 
work these surfaces on pair tools, it will be very easy to reduce 
the third surface, so as to make it equal to the second, by mak- 
ing such a corresponding change in the fourth surface, as shall 
still preserve the same focal length, both for the flint lens singly, 
and for the compound focus. We have only to consider 2*22 
inches as the given radius, 4*64 as the focal length, the index be- 
ing 1*601, and to find the corresponding fourth surface, by the 
rule given for that purpose, viz. (Rule 9 art. 14.) 
Focal length = 4*64 ; Dec. of index = *601 ; 
4*64 x *601 = 2*78864 = 1st product, 
2*22 = given radius, 
2*78864 x 222 = 6*19047 = dividend, 
2*788 — 2*22 - *568 = divisor, 
568) 6*19047 (10*896 = rad. 4th surface. 
